Images and contours

Let us take a look at some examples of visualizing arrays as images. The following function will create a matrix of color values for the Mandelbrot fractal. Here we consider a fixed point iteration, that depends on a complex parameter c:

Depending on the choice of this parameter it may or may not create a bounded sequence of complex values z_n .

For every value of c, we check if z_n exceeds a prescribed bound. If it remains below the bound within maxit iterations, we assume the sequence to be bounded.

Note how, in the following piece of code,meshgrid is used to generate a matrix of complex parameter values c:

def mandelbrot(h,w, maxit=20):
    X,Y = meshgrid(linspace(-2, 0.8, w), linspace(-1.4, 1.4, h))
    c = X + Y*1j
    z = c
    exceeds = zeros(z.shape, dtype=bool)

    for iteration in range(maxit):
        z  = z**2 + c
        exceeded = abs(z) > 4
        exceeds_now = exceeded & (logical_not(exceeds))  
...